Energy representation method for ultrasonic vibration assisted machining of high temperature alloy by longitudinal and torsional composite vibration

Abstract

The application provides an energy characterization method for high-temperature alloy longitudinal-torsional composite ultrasonic vibration assisted machining, which is characterized by the following aspects: based on the superposition of point motion trajectory equations of tool spindle rotation, cutting motion, longitudinal ultrasonic vibration and torsional ultrasonic vibration and the strain rate of a shearing area, and the ultrasonic vibration energy transmitted by a cutting edge within corresponding cutting time, the ultrasonic vibration energy of high-temperature alloy longitudinal-torsional composite ultrasonic vibration assisted machining is characterized, and in addition, the contact characteristics of the tool and the workpiece are considered, so that the input energy of high-temperature alloy longitudinal-torsional composite ultrasonic assisted machining can be better regulated and controlled, so as to adjust the characteristics and microstructure of the material, and finally improve the performance of the machined workpiece.

Description

Technical Field

[0001] This invention relates to the field of ultrasonic vibration-assisted machining technology, and in particular to an energy characterization method for longitudinal-torsional composite ultrasonic vibration-assisted machining of high-temperature alloys. Background Technology

[0002] Nickel-based superalloys, as key materials for next-generation aero-engine components, face challenges during milling due to uncontrollable non-uniform plastic flow and abrupt changes in the hardened layer, leading to uncontrollable surface damage and subsurface structural instability. Due to their high hardness and strength, nickel-based superalloys generate high-level milling heat accumulation in the machining center region, creating a mechanical-thermal coupling field with high dynamic load impact and high temperature gradient. When ultrasonic vibration-assisted machining is used, the intervention of high-frequency vibration impact generates a unique machining mechanism characterized by high strain rate fluctuations, high loading rates, and high-frequency vibration energy during milling. This increases the complexity of the mechanical properties of the material shear zone and alters the material removal mechanism. Essentially, this can be attributed to the dynamic damage, chip generation, and surface creation processes of the workpiece surface and near-surface material under high strain rates. While existing ultrasonic vibration-assisted machining can improve material machinability, the lack of a critical energy threshold and insufficient control mechanisms make it difficult to achieve precise matching of energy input and material response. Summary of the Invention

[0003] The purpose of this invention is to address the shortcomings of the aforementioned background technology by providing a method for characterizing ultrasonic vibration energy during longitudinal-torsional composite ultrasonic vibration-assisted machining of high-temperature alloys. This method aims to help realize a controllable induction mechanism of ultrasonic vibration energy on the surface formation properties of workpieces, thereby improving the machining performance of high-temperature alloys, especially nickel-based high-temperature alloys.

[0004] To achieve the above objectives, the present invention provides an energy characterization method for longitudinal-torsional composite ultrasonic vibration-assisted machining of high-temperature alloys, comprising:

[0005] S1. Establish the function of the cutting edge position change with time in longitudinal-torsional composite ultrasonic vibration assisted machining. Based on the two motions of spindle rotation and cutting feed applied by the tool, longitudinal ultrasonic vibration and torsional ultrasonic vibration, calculate the functional expressions of the motion velocity and acceleration of the mass point according to the motion trajectory equation, and then calculate the strain rate of the shearing region.

[0006] S2, Derive the theoretical expression for ultrasonic vibration energy output, regard the amplitude transformer and the cutter as a uniform isotropic solid medium, the cutter and the amplitude transformer form a fixed integral connection, ignore the mechanical loss in the vibration transmission process, the longitudinal vibration and torsional vibration have the same resonant frequency and the phase difference is zero, the mathematical superposition of the longitudinal vibration and torsional vibration is taken as the total ultrasonic vibration energy of the longitudinal-torsional composite ultrasonic vibration.

[0007] S3, construct a constitutive model of shear flow stress in the shear region of the workpiece during longitudinal-torsional composite ultrasonic vibration assisted machining, and obtain the constitutive relationship of shear flow stress;

[0008] S4, calculate the length of the viscous zone, the local friction coefficient of the sliding zone, the global friction coefficient of the stick-slip zone, the friction force, and the total contact length of the tool and chip under longitudinal torsion combined ultrasonic vibration assisted machining;

[0009] S5, combined with S2-S4, characterizes the ultrasonic vibration energy of longitudinal-torsional composite ultrasonic vibration-assisted machining of high-temperature alloys, and uses ultrasonic vibration energy as a medium to regulate the machining process and material properties.

[0010] Furthermore, when establishing the function of the cutting edge position versus time in longitudinal-torsional composite ultrasonic vibration assisted machining in S1, a global coordinate system is established at the center of the tool bottom. At the same time, in the cutting tool Establish a local reference coordinate system on each cutting edge. The analysis is based on the global coordinate system and the local reference coordinate system.

[0011] Furthermore, when the tool applies both spindle rotation and cutting feed motions, the first... Point on each cutting edge The equation of the trajectory is:

[0012]

[0013] in, It is the tool feed rate. For the tool radius, Main spindle speed and These represent the total number of cutting edges and the number of cutting edges of the tool, respectively. One cutting edge, and .

[0014] Furthermore, when longitudinal ultrasonic vibration is applied to the cutting tool, the first Point on each cutting edge The equation of the trajectory is:

[0015]

[0016] in, It is the longitudinal ultrasonic amplitude. It is the ultrasonic vibration frequency. The initial phase angle of the longitudinal ultrasonic vibration.

[0017] Furthermore, when torsional ultrasonic vibration is applied to the cutting tool, the tool generates high-frequency reciprocating rotation in the circumferential direction. The expressions for the torsional vibration displacement and linear velocity are as follows:

[0018]

[0019] in, To torsion ultrasonic amplitude;

[0020] Thus, the angular velocity of the torsional ultrasonic vibration is obtained. and angle expression:

[0021]

[0022] The angle generated by the torsional ultrasonic vibration Angle of rotation of the tool in the same time period By superimposing the values, the total rotation angle of the tool at a certain time during the machining process can be obtained. for:

[0023]

[0024] This yields the result that during torsional ultrasonic vibration, the cutting tool... The equation of the trajectory of a point on the cutting edge is:

[0025] .

[0026] Furthermore, in S1, the first step of longitudinal-torsional composite ultrasonic vibration-assisted machining is established. Point on each cutting edge Equation of the trajectory of motion:

[0027]

[0028] in, To reverse the initial phase angle of the ultrasonic vibration, and .

[0029] Furthermore, a numerical model of strain rate during one tool pass cycle in longitudinal-torsional combined ultrasonic vibration assisted machining was established in S1.

[0030] Furthermore, the energy density of the sound wave in the propagation medium in S2 is:

[0031]

[0032] Ultrasonic waves propagate in a medium in the form of sinusoidal waves; therefore, the average energy density of an ultrasonic wave over one cycle is:

[0033]

[0034] in, The vibration period of the ultrasound.

[0035] In S2, the average density of the amplitude transformer and the cutter is used as the density of the propagation medium. The density of the amplitude transformer, The density of the cutting tool.

[0036] Furthermore, the cutting edge in S2 superior Point at cutting time Internally transmitted ultrasonic vibration energy:

[0037] .

[0038] Furthermore, in S3, the constitutive relationship of shear flow stress in the shear region of the workpiece assisted by longitudinal-torsional composite ultrasonic vibration is used to calculate the shear flow stress under different conditions, draw the correspondence between shear flow stress and shear strain and analyze it. In S4, the contact friction behavior of the tool-chip interface is analyzed based on the obtained viscous zone length, local friction coefficient of the sliding zone, global friction coefficient of the stick-slip zone, friction force and total contact length of the tool and chip under longitudinal-torsional composite ultrasonic vibration assisted machining.

[0039] The above-described solution of the present invention has the following beneficial effects:

[0040] The present invention provides an energy characterization method for ultrasonic vibration-assisted machining of high-temperature alloys. Based on the point motion trajectory equation of the superposition of tool spindle rotation, cutting motion, longitudinal ultrasonic vibration and torsional ultrasonic vibration, strain rate of the shearing region, and ultrasonic vibration energy transmitted by the cutting edge during the corresponding cutting time, the ultrasonic vibration energy of longitudinal-torsional ultrasonic vibration-assisted machining of high-temperature alloys is characterized. In addition, the contact characteristics between the tool and the workpiece are also considered, so as to better control the input energy of longitudinal-torsional ultrasonic vibration-assisted machining of high-temperature alloys, thereby regulating the material properties, microstructure and other properties, and ultimately improving the performance of the machined workpiece.

[0041] Other beneficial effects of the present invention will be described in detail in the following detailed description section. Attached Figure Description

[0042] Figure 1 This is a flowchart of the steps of the present invention;

[0043] Figure 2 This is a schematic diagram of the processing equipment corresponding to the present invention;

[0044] Figure 3 This is a schematic diagram of the workpiece's undeformed cutting thickness according to the present invention;

[0045] Figure 4 This is a graph showing the change in workpiece surface cutting temperature over time according to the present invention.

[0046] Figure 5 This is a schematic diagram of material deformation removal in the shear region according to the present invention;

[0047] Figure 6 This is a schematic diagram of the stress distribution at the chip-tool interface according to the present invention. Detailed Implementation

[0048] The following specific examples illustrate the implementation of this disclosure. Those skilled in the art can easily understand other advantages and effects of this disclosure from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this disclosure, and not all of them. This disclosure can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this disclosure. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this disclosure, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this disclosure.

[0049] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this disclosure, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.

[0050] It should also be noted that the illustrations provided in the following embodiments are merely schematic representations of the basic concept of this disclosure. The illustrations only show components relevant to this disclosure and are not drawn according to the actual number, shape, and size of components in implementation. In actual implementation, the type, quantity, and proportion of each component can be arbitrarily changed, and the component layout may be more complex. Furthermore, specific details are provided in the following description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.

[0051] like Figure 1 As shown, embodiments of the present invention provide an energy characterization method for longitudinal-torsional composite ultrasonic-assisted machining of high-temperature alloys, and the corresponding machining equipment is as follows: Figure 2As shown, the device includes a wireless transmission disk, an ultrasonic tool holder, a transducer, a longitudinal-torsional amplitude transformer, and a cutting tool (end mill). The equipment utilizes the magnetostrictive effect of the piezoelectric ceramic sheet in the transducer to convert an electrical signal of a certain excitation frequency into a sinusoidally varying high-frequency mechanical vibration. The longitudinal-torsional composite vibration is achieved by creating a certain number, angle, and fixed aspect ratio of helical grooves in the amplitude transformer, thereby converting the vibration at the tool output end from one-dimensional longitudinal vibration into a longitudinal-torsional composite vibration containing both longitudinal and torsional vibration modes. Therefore, the machining process consists of a mixture of longitudinal-torsional composite ultrasonic vibration, feed motion, spindle rotation, and other motion modes, resulting in a highly complex movement of the tool's cutting edge.

[0052] Based on this, the energy characterization method for longitudinal-torsional composite ultrasonic-assisted machining of high-temperature alloys provided in this embodiment requires first establishing the tool tip (cutting edge) position for longitudinal-torsional composite ultrasonic vibration-assisted machining, then deriving the theoretical expression for ultrasonic vibration energy output, and finally quantifying the ultrasonic vibration energy transmitted from the cutting edge to the workpiece.

[0053] When establishing the cutting edge position for longitudinal-torsional composite ultrasonic vibration assisted machining, a global coordinate system as shown in the figure is established at the center of the tool bottom. At the same time, in the cutting tool Establish a local reference coordinate system on each cutting edge. Randomly select the first... A point on the cutting edge As the object of analysis, during machining, the tool is subjected to two motions: spindle rotation and cutting feed. The analysis focuses on the first motion. Point on each cutting edge The trajectory of the motion is obtained, and its trajectory equation is:

[0054] (1)

[0055] in, It is the tool feed rate (mm / min). The radius of the tool (mm) Spindle speed (r / min) and These represent the total number of cutting edges and the number of cutting edges of the tool, respectively. One cutting edge, and .

[0056] When the cutting tool is subjected to longitudinal ultrasonic vibration, the motion trajectory equation of the cutting edge is expressed as:

[0057] (2)

[0058] in, It is the longitudinal ultrasonic amplitude (μm). It is the ultrasonic vibration frequency (kHz). The initial phase angle (rad) of the longitudinal ultrasonic vibration.

[0059] The increase in torsional ultrasonic vibration causes the tool to undergo high-frequency reciprocating rotation in the circumferential direction. Based on the analysis of the vibration cutting mechanism, the expressions for torsional vibration displacement and linear velocity are obtained as follows:

[0060] (3)

[0061] in, The amplitude of the torsional ultrasound is (μm).

[0062] The angular velocity of torsional ultrasonic vibration is obtained by deriving equation (3). and angle expression:

[0063] (4)

[0064] The angle generated by the torsional ultrasonic vibration Angle of rotation of the tool in the same time period By superimposing the values, the total rotation angle of the tool at a certain time during the machining process can be obtained. for:

[0065] (5)

[0066] This leads to the derivation of the cutting tool's first... The equation of the trajectory of a point on the cutting edge is:

[0067] (6)

[0068] Based on the analysis of the longitudinal and torsional ultrasonic vibration cutting edge motion trajectory, the motion trajectory equation of a point on the longitudinal-torsional combined ultrasonic vibration cutting edge is established as follows:

[0069] (7)

[0070] in, The initial phase angle (rad) of the torsional ultrasonic vibration is given. Considering the amplitude transformer is a helical groove type single-excitation ultrasonic vibration amplitude transformer, therefore... .

[0071] Therefore, in this embodiment, the movement trajectory of the cutting edge includes both longitudinal vibration and rotation. This motion pattern can achieve intermittent contact between the cutting edge and the chip in the circumferential direction under certain conditions. During longitudinal-torsional composite ultrasonic vibration assisted machining, the cutting edge will rotate or change speed in the torsional direction, and generate longitudinal high-frequency vibration in the axial direction. Its extremely large motion acceleration means that huge inertial loads and high-frequency impact energy act on the shear region of the material, causing the material in the shear region to bear huge instantaneous strain rates.

[0072] Specifically, the strain rate relationship in longitudinal-torsional composite ultrasonic vibration-assisted machining is shown below:

[0073] (8)

[0074] in, In response, The cutting speed is (m / s). The (instantaneous) undeformed cutting thickness (mm) of the workpiece.

[0075] According to equation (8), the cutting speed and the undeformed cutting thickness during the machining process need to be calculated. The cutting speed of the cutting edge during the machining process is... Figure 2 The coordinate system shown can be decomposed into , and There are three components, which can be obtained by differentiating the equation of the spatial motion trajectory of the cutting edge. Therefore, by differentiating equation (7), the cutting speed components of the cutting edge are as follows:

[0076] (9)

[0077] Therefore, the actual cutting speed at a point on the cutting edge during the machining process can be obtained as follows:

[0078] (10)

[0079] Figure 3 The diagram shows the established undeformed cutting thickness. A fixed coordinate system (workpiece coordinate system) OXYZ is established with the workpiece as the reference, which is... Figure 2 Maintain consistency with the central government, while also in Figure 3 A moving coordinate system (tool coordinate system) that varies with time is established with the tool rotation center as the reference. Assuming in At that moment, the The positions of the cutting edges are shown as those of the dark-colored tool in the figure. The cutting edges are... The angular displacement of the axis is expressed as:

[0080] (11)

[0081] Depend on Figure 3 As shown in the image, the light-colored knife represents the first... The cutting edge is Location at any given moment For the previous cutting edge and angular displacement, where This represents the time lag associated with the two cutting edges. From this, we can obtain... Undeformed cutting thickness at all times Equivalent to the first moment Point where the cutting edge is located and the The cutting edge is Location at time The distance between them.

[0082] exist Time, Point The coordinates in the fixed coordinate system OXYZ are:

[0083] (12)

[0084] in, Let be the coordinates of the origin of the moving coordinate system in the fixed coordinate system. The coordinates of the tool center in the moving coordinate system are given.

[0085] exist Time, Point The coordinates in the fixed coordinate system OXYZ are:

[0086] (13)

[0087] in, for The coordinates of the origin of the moving coordinate system in the fixed coordinate system at any given time. for The coordinates of the tool center in the moving coordinate system at any given time.

[0088] At the same time, point exist Time can also be represented in a fixed coordinate system as:

[0089] (14)

[0090] Clearly, equations (13) and (14) have the same meaning. Furthermore, the tool coordinate system is relative to the workpiece coordinate system in the X direction. The feed rate performs the feed motion, resulting in the following relationship:

[0091] (15)

[0092] The simultaneous equations (13), (14), and (15) are obtained through deduction and simplification. The expression for the undeformed cutting thickness at time t is:

[0093] (16)

[0094] Among them, the undeformed cutting thickness The change in static cutting thickness caused by feed rate and the change in dynamic cutting thickness caused by regeneration effect The result of the superposition is expressed as:

[0095] (17)

[0096] in, This represents the feed rate per tooth of the cutting tool (mm).

[0097] It should be noted that the cutting edge undergoes a relatively long-period subcycloidal motion with the spindle rotation, and a relatively short-period reciprocating motion with the ultrasonic vibration. Since the ultrasonic vibration period is relatively small compared to the spindle rotation period, the time hysteresis can be approximated as equal to the tool pass period, i.e.:

[0098] (18)

[0099] Substituting the equation of the motion trajectory of a point on the cutting edge from equation (7) into equation (17), and simultaneously solving the other known terms, we can obtain the formula for calculating the undeformed cutting thickness under longitudinal-torsional combined ultrasonic vibration assisted machining, namely:

[0100] (19)

[0101] Combining equations (9), (10), and (19) and substituting them into equation (8), a numerical model of the strain rate in one tool pass cycle of longitudinal-torsional composite ultrasonic vibration-assisted machining is established, as shown below:

[0102] (20)

[0103] Numerical simulations revealed that the strain rate under longitudinal-torsional combined ultrasonic vibration assisted machining exhibits an approximately sinusoidal trend, with peak values ​​exceeding two orders of magnitude of those under conventional machining. The peak strain rate increases continuously with increasing ultrasonic amplitude. The higher strain rate in longitudinal-torsional combined ultrasonic vibration assisted machining implies a smaller peak instantaneous undeformed cutting thickness compared to conventional machining. This suggests a smaller instantaneous cutting amount and force at the cutting edge, resulting in a more refined material removal process. This indicates that the intervention of high-frequency ultrasonic vibration alters the cutting speed and undeformed cutting thickness during machining, thereby changing the range of strain rate values. Higher strain rates contribute to improved production efficiency and reduced cutting forces and power consumption. The strain rate profoundly affects material removal, especially the characteristics of the material shear region directly in contact with the cutting edge.

[0104] As described above, longitudinal-torsional ultrasonic vibration-assisted machining exhibits extremely high motion acceleration and machining strain rates, implying that enormous inertial loads and high-frequency impact energy act on the shear region of the material. Therefore, in order to quantitatively analyze the ultrasonic vibration energy imparted to the cutting tool, theoretical modeling and quantitative analysis of the ultrasonic vibration energy of the cutting edge are necessary.

[0105] When theoretically modeling and quantifying the ultrasonic vibration energy of a cutting edge, it is considered that the ultrasonic vibration is transmitted and amplified by an amplitude transformer, and then acts on the workpiece through the tool, which belongs to the propagation of sound waves in a solid medium. The essence of propagation theory is that energy is transferred through the displacement of protons (unit infinitesimal elements). Therefore, the formula for energy density in a solid medium and the expression for acoustic energy can be calculated by differentiating the plane wave function.

[0106] It should be noted that the derivation of the energy density equation in this embodiment is based on the following assumptions: the amplitude transformer and the cutter are considered as homogeneous isotropic solid media; the cutter and the amplitude transformer are fixedly (integratedly) connected; and mechanical losses during vibration transmission are ignored. Since the longitudinal and torsional vibrations are generated from the same source of excitation, they have the same resonant frequency; and they are simultaneously excited by the helical groove structure on the amplitude transformer, therefore the phase difference between them is zero. Based on this, in this embodiment, when calculating the output energy of the system, the mathematical superposition of the two vibrations is used as the total output energy of the longitudinal-torsional composite ultrasonic vibration.

[0107] Specifically, the wave equation for a unit infinitesimal element in a solid medium (i.e., the amplitude transformer) with respect to time and displacement is as follows:

[0108] (twenty one)

[0109] in, The amplitude of the sound wave. Circular wave number , Angular frequency , The speed at which sound waves propagate in a solid medium. is the vibration frequency of the sound wave.

[0110] For a unit infinitesimal element, its displacement function is obtained by taking the partial derivative of the distance from the wave equation above:

[0111] (twenty two)

[0112] Similarly, the velocity of a unit infinitesimal element is the partial derivative of its displacement function with respect to time, as shown below:

[0113] (twenty three)

[0114] When sound waves propagate in an acoustic system, the unit element in the medium vibrates along with the propagation of the sound waves, thus acquiring kinetic energy (dEk). Furthermore, the unit element is constantly compressed and stretched by adjacent unit elements, undergoing elastic deformation, and thus acquiring elastic potential energy (dEp). The sum of the kinetic energy and elastic potential energy of the unit element represents its total energy content. Based on the kinetic energy expression of a unit element in physics, and combined with equation (10), the expressions for the longitudinal and torsional vibration kinetic energy of the unit element are obtained:

[0115] (twenty four)

[0116] in, This refers to the longitudinal ultrasonic amplitude. To reverse the ultrasonic amplitude, For the density of the transmission medium, The volume of a unit infinitesimal element. , These represent the vibrational kinetic energy of a unit mass element in the longitudinal and torsional directions, respectively.

[0117] Assume the unit infinitesimal element at time t The elongation rate is Based on knowledge of materials mechanics, the relationship between stress and strain of a unit infinitesimal element can be obtained:

[0118] (25)

[0119] in, The stress of a unit infinitesimal element. The strain is a unit infinitesimal element. The Young's modulus of the transmission medium. It represents the cross-sectional area of ​​a unit micro-element.

[0120] Since the transmission medium is an elastic medium, its microscopic elastic deformation conforms to Hooke's Law. Furthermore, the wave velocity and Young's modulus in the transmission medium have the following relationship, from which we can derive:

[0121] (26)

[0122] In the formula, is the elastic coefficient of the transmission medium.

[0123] Combining equations (12) and (13), we obtain the elastic potential energy of the unit infinitesimal element in the longitudinal and torsional directions as follows:

[0124] (27)

[0125] in, The longitudinal elastic potential energy of a unit infinitesimal element. The torsional elastic potential energy is expressed as a unit infinitesimal element.

[0126] During the propagation of ultrasound, the total mechanical energy (sound energy) of a unit micro-element is the sum of vibrational kinetic energy and elastic potential energy:

[0127] (28)

[0128] Therefore, the energy density of sound waves in the propagation medium can be obtained:

[0129] (29)

[0130] Typically, ultrasound propagates in a medium as a sinusoidal wave; therefore, the average energy density of ultrasound over one cycle is:

[0131] (30)

[0132] in, This is the vibration period of the ultrasonic wave.

[0133] As mentioned above, the average energy density of ultrasound is only related to the density of the propagation medium. Therefore, in this embodiment, the average density of the amplitude transformer and the cutting tool is used as the density of the propagation medium. Figure 4 The workpiece surface measured at a cutting speed of 100 m / min The change of cutting temperature over time. During the cutting process, The instantaneous temperature at a point first rises and then falls, divided into a cutting temperature rise stage and a cooling stage. Since the workpiece temperature rises during the cutting stage, the cutting time equals the temperature rise time. Let's assume that at any cutting speed... The cutting time of the point is Then the tool during cutting time Internal action The ultrasonic vibration energy of the point (at this time) The expression for a point (considered to have a unit volume) is:

[0134] (31)

[0135] in, The density of the amplitude transformer, The density of the cutting tool.

[0136] By combining the motion trajectory equations of each point on the cutting edge, the cutting edge can be obtained. superior Point at cutting time Internally transmitted ultrasonic vibration energy:

[0137] (32)

[0138] During the cutting process, the cutting tool continuously cuts and compresses the workpiece material through its cutting edge, ultimately removing the material. Ultrasonic vibration energy is continuously transmitted to the workpiece surface through the cutting tool. Therefore, the acoustic energy transmitted through the cutting tool and accumulated on the workpiece surface during the cutting time can be considered as ultrasonic vibration energy acting on the surface layer of the workpiece material. Ultrasonic vibration energy is a unique processing property of longitudinal-torsional composite ultrasonic vibration-assisted machining, capable of influencing material properties and altering its microstructure.

[0139] For example, the high strain rate and high-frequency ultrasonic vibration energy involved in longitudinal-torsional combined ultrasonic vibration assisted machining will affect the deformation behavior of the material in the shear region of the workpiece. Therefore, in this embodiment, a constitutive model of the shear flow stress in the shear region of the workpiece is further constructed to analyze the deformation behavior of the material in the shear region of the workpiece.

[0140] Material constitutive models can be categorized into three main types: empirical models, semi-empirical models, and physical models. Among these, the Johnson-Cook (JC) model, an empirical model, can perform a comprehensive coupled analysis of material flow stress, strain hardening, strain rate hardening, and thermal softening effects during deformation. Furthermore, its form is relatively simple, and model parameters are easy to identify, making it the most widely used model in metal cutting. Therefore, in this embodiment, the JC model is chosen to construct the constitutive relation of the workpiece's shear region. The JC model represents the material flow stress through strain rate hardening, strain hardening, and temperature softening terms, and its basic form is shown in the following equation:

[0141] (33)

[0142] in, The equivalent flow stress of the material, The equivalent plastic strain of the material, The equivalent plastic strain rate of the material. For material temperature, The melting point of the material. and These are the reference strain rate and the reference temperature, which are typically set to room temperature. Five model constants. These represent the initial yield strength, hardening modulus, strain hardening exponent, strain rate sensitivity coefficient, and thermal softening coefficient of the material, respectively. For example, for the high-temperature alloy GH4169, we can take... 963MPa 937, 0.022, 0.333, 1.3, and the melting point of the high-temperature alloy GH4169 is 1573K, that is... 1573K, take another =0.002s -1 , 293.15K.

[0143] To establish a more accurate constitutive relation, define The functional relationship is used to introduce strain compensation into the strain hardening exponent term. Furthermore, to consider the influence of adiabatic temperature rise in the thermal softening term, based on existing research on shear surface temperature rise models, the following expression is obtained:

[0144] (34)

[0145] in, This indicates the cutting temperature (i.e., initial temperature) of the material in the shearing zone of the workpiece. This represents the proportion of shear energy converted into enthalpy, for example, 87.4%. It is the temperature rise caused by plastic strain in the shear region of the workpiece. For material density, For cutting width, For the specific heat of the material, For cutting depth, Shear angle, The rake angle of the tool. This is the heat distribution coefficient for the shearing processing area, for example, 0.267.

[0146] In this embodiment, the relationship between equivalent plastic strain, strain rate, and strain hardening exponent is obtained through nonlinear fitting. Then, the strain hardening exponent under arbitrary equivalent plastic strain is solved through numerical simulation to obtain the undetermined coefficients. At the same time, the temperature sensitivity coefficient is corrected and solved, and the optimized and improved JC model is obtained by simplification. Thus, the constitutive relation is as shown in the following equation:

[0147] (35)

[0148] In one specific embodiment, the undetermined coefficients included in equation (35) for the high-temperature alloy GH4169 can take the values ​​shown in Table 1:

[0149] Table 1 Undetermined coefficients of constitutive relation for GH4169

[0150]

[0151] Understandably, during machining, high-frequency impact and vibration compression concentrate on the workpiece's shear region, causing the material to transition from elastic deformation to plastic deformation, and then fracture and fail at the shear slip zone, forming chips. Therefore, the shear flow stress in the shear region is not only related to the material's normal stress constitutive relation but is also influenced by the tool structure and acoustic parameters. Based on the yield criterion for the principal stresses of elastic-plastic materials proposed by Von-Mises, the shear flow stress in the workpiece's shear region is calculated. Normal stress and shear strain Positive strain The relational conversion is expressed as follows:

[0152] (36)

[0153] Combining (35) and (36), the constitutive relationship of shear flow stress in the shear region of the workpiece can be obtained:

[0154] (37)

[0155] in, and They are the shear strain rates (s) -1 ) and reference shear strain rate (s -1 ),For example Take 0.004s -1 .

[0156] Equation (37) shows that the shear flow stress of the material is closely related to the shear strain and shear strain rate in the shear region, while the shear strain and shear strain rate depend on the tool parameters and the tool-chip cutting model during orthogonal cutting. Therefore, in this embodiment, combined with the existing tool-chip cutting model, the deformation and shear stress distribution relationship of the unit material in the shear region under ultrasonic vibration are further established, such as... Figure 5 As shown in the figure. The area enclosed by the dashed line is the strip-shaped shear region, and line segment AB is the center of the shear region. From the geometric relationships in the figure, the expression for the shear angle can be derived as follows:

[0157] (38)

[0158] in, The thickness of the chips in the shearing zone (mm).

[0159] Chip thickness in the shearing zone and undeformed cutting thickness There exists an empirical relation as follows:

[0160] (39)

[0161] in, The coefficient is related to the average aspect ratio of the material chips, and its value is usually between 6 and 12. In this embodiment, it is 8.5. For the calculation formula of the instantaneous undeformed cutting thickness under longitudinal torsion combined ultrasonic vibration assisted machining, please refer to formula (19).

[0162] Furthermore, it should be noted that during longitudinal-torsional combined ultrasonic vibration assisted machining, the tool undergoes high-frequency reciprocating motion in the axial direction, causing periodic changes in the cutting depth. Therefore, the actual cutting depth of the tool... It can be represented as:

[0163] (40)

[0164] Substituting equations (40) and (39) into equation (38), we obtain the expression for the shear angle as follows:

[0165] (41)

[0166] Average shear stress on shear plane AB It can be expressed by the following formula:

[0167] (42)

[0168] in, It is the shearing force, which can be measured by milling experiments as the main cutting force. and cutting depth resistance The calculation is expressed as:

[0169] (43)

[0170] Average shear strain of shear plane AB It can be expressed by the following formula:

[0171] (44)

[0172] Therefore, substituting equation (41) into equation (44) yields the average shear strain in the shear region.

[0173] According to current tool-chip cutting model theory, the average shear strain rate and shear velocity of the shear surface AB are... Proportional to the length of the shear band AB Inversely proportional. Therefore, the expression for the average shear strain rate and related parameters can be obtained as follows:

[0174] (45)

[0175] in, The ratio of the length of the shear plane AB to the thickness of the first shear region is calculated by the following formula:

[0176] (46)

[0177] in, and These are the shearing region points. and points Hydrostatic stress at the location, , These are equivalent stress and equivalent strain, respectively.

[0178] Combining equations (45) and (46), the shear strain rate in the shear region can be obtained. The expression:

[0179] (47)

[0180] Combining equations (44), (47), and (37), the constitutive relationship (equation) of shear flow stress in the shear region of the workpiece under longitudinal-torsional composite ultrasonic vibration assisted machining can be obtained:

[0181] (48)

[0182] According to equation (48), the shear flow stress under different conditions can be calculated, and the correspondence between shear flow stress and shear strain can be plotted. It can be seen that the shear flow stress in the shear region first increases rapidly with the increase of shear strain. In this process, the deformation of the material is mainly dominated by the strain hardening effect, which makes it quickly reach the yield point. Subsequently, the material enters the plastic deformation stage, and plastic deformation energy begins to accumulate continuously inside the material. At the same time, the accumulated thermal softening effect counteracts the strain hardening effect, and the shear flow stress remains relatively constant. As the material deformation accumulates, the material undergoes plastic constitutive instability fracture failure, resulting in a rapid decrease in shear flow stress.

[0183] Simultaneously, it can be observed that with the increase of shear strain rate, the stress increase in the elastic deformation stage of the material remains basically unchanged, while the shear flow stress in the plastic deformation stage continuously increases. It was also found that the duration of plastic deformation becomes longer, i.e., the greater the shear strain rate, the stronger the plastic deformation stage. This indicates that there is a positively correlated shear strain rate enhancement effect in the material deformation process of this embodiment. Furthermore, with the increase of deformation temperature, the shear flow stress in the plastic deformation stage shows a decreasing trend. This is because the increase in deformation temperature leads to the continuous accumulation of thermally activated energy within the material, resulting in enhanced interatomic thermal motion, decreased bonding force, and increased dislocation annihilation, thereby reducing the yield strength of the material. This indicates that the material in this embodiment exhibits a significant high-temperature thermal softening effect during deformation.

[0184] It should be noted that cutting motion is generally considered a plastic shearing behavior, occurring near the contact interface or in the upward shear flow layer, with a stagnant layer near the tool tip. Based on the relative motion of the chip on the tool rake face, the chip-tool interface can be classified into a viscous zone and a sliding zone. The instantaneous relative velocity between the chip and tool in the viscous zone is lower than that in the sliding zone, and the velocity vector in the viscous zone exhibits a chaotic state due to the irregular tearing of the underlying chip material. Furthermore, the shear stress and normal stress distributions differ between the two regions, such as... Figure 6 As shown in the figure, the normal stress is the largest at the cutting edge, decreases with increasing contact length at the tool-chip interface, and finally becomes zero when the chip flows out from the tool rake face. Although the frictional stress in the sliding zone has a similar trend to the normal stress, the frictional stress remains constant in the viscous zone. The following equation represents the widely used stick-slip friction model, where the activation of different frictional states depends on the frictional stress at the tool-chip interface. Whether the shear yield strength of the workpiece material has been reached.

[0185] (49)

[0186] in, This represents the ultimate shear stress in the viscous region. The local friction coefficient of the sliding zone. For the normal stress at the chip / tool ​​interface, This is the distance (mm) from the tip of the cutting tool to the front face. The length of the contact between the cutter face and the chip (mm) is the length of contact between the cutter face and the chip. This represents the length of the viscous zone (mm). When the frictional stress is greater than or equal to the ultimate shear stress, viscous friction dominates; otherwise, sliding friction dominates. The normal stress at the chip-tool interface is also considered. It can be expressed as the following formula:

[0187] (50)

[0188] in, The normal contact stress at the tool tip (MPa) This is a correction factor, for example, it can be 3.2.

[0189] Please refer to it again. Figure 6 In cutting tools, the viscous and sliding zones coexist on the rake face. The total length of the viscous and sliding zones is called the total length of the chip-tool contact, and there is a certain numerical proportional relationship between the two. Referring to existing research, the expression for calculating the length of the viscous zone is derived as follows:

[0190] (51)

[0191] in, Indicates the shearing angle during machining. Indicates the rake angle of the milling cutter. This represents the average shear strain in the shear region. The shear stress at the inlet of the shear region can be calculated by applying boundary conditions to the strain rates at the inlet and outlet of the shear region, based on the constitutive equation of shear flow stress in equation (48).

[0192] Assuming the normal stress is uniformly distributed on the shear plane, and using the torque at the blade tip for balance, the total contact length is:

[0193] (52)

[0194] in, Indicates the chip flow angle. Indicates the rake angle of the cutting tool. Indicates the normal friction angle. It can be defined by the following formula:

[0195] (53)

[0196] in, The shear flow angle of the material can be represented by a velocity relationship calculation method provided by existing technology:

[0197] (54)

[0198] Consider along the contact length Pressure distribution can This is related to the normal force acting on the rake face along the normal direction. The normal force is also defined based on the shear force on the shear plane. From these two definitions, we can obtain... The expression is:

[0199] (55)

[0200] Based on the continuity of shear stress, in You can get it from there:

[0201] (56)

[0202] Combining equations (56) and (55), the local friction coefficient of the sliding zone can be obtained as follows:

[0203] (57)

[0204] Equation (57) not only yielded the local friction coefficient of the sliding zone, but also the tool-chip contact length on the rake face. and viscous region length The expression for the normal stress at the chip / tool ​​interface. The analytical expression is obtained. Therefore, by simultaneously solving the above equations and integrating the stresses in the sliding and viscous regions respectively, the normal force in the stick-slip region can be obtained. With friction The expression is as follows:

[0205] (58)

[0206] in, Indicates the cutting width.

[0207] According to Coulomb's law of friction, the ratio of the normal force to the frictional force in the stick-slip zone is equal to the global coefficient of friction of the stick-slip zone, and its expression is:

[0208] (59)

[0209] in, It is the apparent friction angle.

[0210] The local friction coefficient of the sliding zone can be obtained from equations (59) and (57), respectively. Global friction coefficient of the stick-slip zone and friction The intervention of ultrasonic vibration alters the undeformed cutting thickness, shear angle, chip flow angle, and average shear strain in the shear zone used in the above formula derivation. The undeformed cutting thickness, shear angle, chip flow angle, and average shear strain in the shear zone have already been derived. Therefore, by substituting these parameters into the corresponding formulas and simultaneously solving related equations, the length of the viscous zone under longitudinal-torsional combined ultrasonic vibration-assisted machining can be obtained. Local friction coefficient of the sliding zone Global friction coefficient of the stick-slip zone Friction and total contact length of the cutting tool and chips Calculations revealed that the contact interface parameters decreased with increasing ultrasonic vibration amplitude. In the viscous region, the tool tip continuously cuts and compresses the workpiece material, causing shear deformation and adhesion to the tool tip. As the cutting action continues, the workpiece material is sheared away, i.e., the chips slide out along the tool rake face, thus forming a sliding zone. Simultaneously, the application of ultrasonic vibration reduces the frictional behavior between the chips and the rake face in the sliding zone, accelerating chip flow and removal. The continuous decrease in the length of the viscous zone and the chip-tool contact length indicates that high-frequency ultrasonic vibration improves the viscous behavior of the workpiece material at the tool tip on the rake face, accelerating the removal of the workpiece material from the rake face, thereby leading to an overall decrease in the length of the viscous zone and the chip-tool contact length. As previously stated, the shear zone under longitudinal-torsional combined ultrasonic vibration-assisted machining exhibits a higher shear strain rate, which is beneficial for the shear deformation and fracture of the workpiece material. Therefore, increasing the ultrasonic amplitude reduces the adhesion behavior of the material in the viscous zone and improves the chip removal behavior in the sliding zone, thereby reducing the length of the viscous zone and the local friction in the sliding zone, ultimately leading to a decrease in the global friction coefficient and friction force. Furthermore, it can be concluded that applying ultrasonic vibration can reduce the intensification of material adhesion and friction behavior caused by large cutting depths, achieving a better friction state and cutting conditions.

[0211] As described above, the energy characterization method for high-temperature alloy conforming to ultrasonic vibration-assisted machining provided in this embodiment characterizes the ultrasonic vibration energy of high-temperature alloy longitudinal-torsional composite ultrasonic vibration-assisted machining based on the point motion trajectory equation of the superposition of tool spindle rotation, cutting motion, longitudinal ultrasonic vibration and torsional ultrasonic vibration, strain rate of the shearing region, and ultrasonic vibration energy transmitted by the cutting edge during the corresponding cutting time. In addition, the contact characteristics between the tool and the workpiece are also considered, so as to better control the input energy of high-temperature alloy longitudinal-torsional composite ultrasonic vibration-assisted machining, thereby adjusting the material properties, microstructure, etc., and ultimately improving the performance of the machined workpiece.

[0212] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification. Furthermore, an increase in longitudinal ultrasonic amplitude means a longer cutting path within the same interval, resulting in a significant reduction in instantaneous cutting thickness under the condition of a constant cutting depth. An increase in torsional ultrasonic amplitude affects the separation characteristics between the tool and the workpiece; that is, the larger the torsional ultrasonic amplitude, the more pronounced the rotation of the cutting edge, and the higher the degree of separation between the tool and the workpiece. In addition, a higher amplitude indicates a more severe impact of the cutting edge on the workpiece surface and a higher loading rate.

[0213] The above embodiments are merely illustrative of several implementation methods of this application, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. An energy characterization method for longitudinal-torsional composite ultrasonic vibration-assisted machining of high-temperature alloys, characterized in that, include: S1. Establish the function of the cutting edge position change with time in longitudinal-torsional composite ultrasonic vibration assisted machining. Based on the two motions of spindle rotation and cutting feed applied by the tool, longitudinal ultrasonic vibration and torsional ultrasonic vibration, calculate the functional expressions of the motion velocity and acceleration of the mass point according to the motion trajectory equation, and then calculate the strain rate of the shearing region. S2, Derive the theoretical expression for ultrasonic vibration energy output, regard the amplitude transformer and the cutter as a uniform isotropic solid medium, the cutter and the amplitude transformer form a fixed integral connection, ignore the mechanical loss in the vibration transmission process, the longitudinal vibration and torsional vibration have the same resonant frequency and the phase difference is zero, the mathematical superposition of the longitudinal vibration and torsional vibration is taken as the total ultrasonic vibration energy of the longitudinal-torsional composite ultrasonic vibration. S3, construct a constitutive model of shear flow stress in the shear region of the workpiece during longitudinal-torsional composite ultrasonic vibration assisted machining, and obtain the constitutive relationship of shear flow stress; S4, calculate the length of the viscous zone, the local friction coefficient of the sliding zone, the global friction coefficient of the stick-slip zone, the friction force, and the total contact length of the tool and chip under longitudinal torsion combined ultrasonic vibration assisted machining; S5, combined with S2-S4, characterizes the ultrasonic vibration energy of longitudinal-torsional composite ultrasonic vibration-assisted machining of high-temperature alloys, and uses ultrasonic vibration energy as a medium to regulate the machining process and material properties. When establishing the function of the cutting edge position versus time in longitudinal-torsional composite ultrasonic vibration assisted machining in S1, a global coordinate system is established at the center of the tool bottom. At the same time, in the cutting tool Establish a local reference coordinate system on each cutting edge. The analysis is based on the global coordinate system and the local reference coordinate system; When the tool applies two motions, spindle rotation and cutting feed, the first... Point on each cutting edge The equation of the trajectory is: in, It is the tool feed rate. For the tool radius, Main spindle speed and These represent the total number of cutting edges and the number of cutting edges of the tool, respectively. One cutting edge, and ; When longitudinal ultrasonic vibration is applied to the cutting tool, the first Point on each cutting edge The equation of the trajectory is: in, It is the longitudinal ultrasonic amplitude. It is the ultrasonic vibration frequency. The initial phase angle of the longitudinal ultrasonic vibration; When torsional ultrasonic vibration is applied to the cutting tool, the tool generates high-frequency reciprocating rotation in the circumferential direction. The expressions for the torsional vibration displacement and linear velocity are: in, To torsion ultrasonic amplitude; Thus, the angular velocity of the torsional ultrasonic vibration is obtained. and angle expression: The angle generated by the torsional ultrasonic vibration Angle of rotation of the tool in the same time period By superimposing the values, the total rotation angle of the tool at a certain time during the machining process can be obtained. for: This yields the result that during torsional ultrasonic vibration, the cutting tool... The equation of the trajectory of a point on the cutting edge is: ； S1 establishes the first longitudinal-torsional composite ultrasonic vibration assisted machining Point on each cutting edge Equation of the trajectory of motion: in, To reverse the initial phase angle of the ultrasonic vibration, and .

2. The energy characterization method for longitudinal-torsional composite ultrasonic vibration-assisted machining of high-temperature alloys according to claim 1, characterized in that, A numerical model of strain rate during one tool pass cycle in longitudinal-torsional combined ultrasonic vibration assisted machining was established in S1.

3. The energy characterization method for longitudinal-torsional composite ultrasonic vibration-assisted machining of high-temperature alloys according to claim 2, characterized in that, The energy density of the sound wave in S2 in the propagation medium is: Ultrasonic waves propagate in a medium in the form of sinusoidal waves; therefore, the average energy density of an ultrasonic wave over one cycle is: in, The vibration period of the ultrasound. In S2, the average density of the amplitude transformer and the cutter is used as the density of the propagation medium. The density of the amplitude transformer, The density of the cutting tool.

4. The energy characterization method for longitudinal-torsional composite ultrasonic vibration-assisted machining of high-temperature alloys according to claim 2, characterized in that, S2 cutting edge superior Point at cutting time Internally transmitted ultrasonic vibration energy: 。 5. The energy characterization method for longitudinal-torsional composite ultrasonic vibration-assisted machining of high-temperature alloys according to claim 4, characterized in that, In S3, the constitutive relationship of shear flow stress in the shear region of the workpiece assisted by longitudinal-torsional composite ultrasonic vibration is obtained. The shear flow stress under different conditions is calculated, and the correspondence between shear flow stress and shear strain is plotted and analyzed. In S4, the contact friction behavior of the tool-chip interface is analyzed based on the obtained viscous zone length, local friction coefficient of the sliding zone, global friction coefficient of the stick-slip zone, friction force, and total contact length of the tool and chip under longitudinal-torsional composite ultrasonic vibration assisted machining.

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